Geodesic
High-Order Time Discretization of The Wave Equation by Nabla-P Scheme.
Hélène Barucq1 ; Henri Calandra2 ; Julien Diaz1 ; Florent Ventimiglia3
1 EPI Magique 3D, INRIA Bordeaux Sud-Ouest, IPRA-LMA.
2 TOTAL Exploration/Production.
3 EPI Magique 3D, INRIA Bordeaux Sud-Ouest, IPRA-LMA and TOTAL Exploration/Production.
ESAIM. Proceedings, Tome 45 (2014), pp. 67-74.

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High-order Discontinuous Galerkin Methods (DGM) are now routinely used for simulation of wave propagation, especially for geophysical applications. However, to fully take full advantage of the high-order space discretization, it is relevant to use a high-order time discretization. Hence, DGM are currently coupled with ADER schemes, which leads to high-order explicit time schemes, but requires the introduction of auxiliary unknowns. The memory can thus be considerably cluttered up. In this work, we propose a new high order time scheme, the so-called Nabla-p scheme. This scheme does not increase the storage costs since it is a single step method which does not require introducing auxiliary unknowns. Numerical results show that for a given accuracy, the new scheme requires less computational burden regarding both the memory and the computational costs than the DG-ADER scheme.
DOI : 10.1051/proc/201445007

Hélène Barucq 1 ; Henri Calandra 2 ; Julien Diaz 1 ; Florent Ventimiglia 3

1 EPI Magique 3D, INRIA Bordeaux Sud-Ouest, IPRA-LMA.
2 TOTAL Exploration/Production.
3 EPI Magique 3D, INRIA Bordeaux Sud-Ouest, IPRA-LMA and TOTAL Exploration/Production. 
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     title = {High-Order {Time} {Discretization} of {The} {Wave} {Equation} by {Nabla-P} {Scheme.}},
     journal = {ESAIM. Proceedings},
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Hélène Barucq; Henri Calandra; Julien Diaz; Florent Ventimiglia. High-Order Time Discretization of The Wave Equation by Nabla-P Scheme.. ESAIM. Proceedings, Tome 45 (2014), pp. 67-74. doi : 10.1051/proc/201445007. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445007/

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